Bifurcation Dodge: Avoidance of a Thermoacoustic Instability under Transient Operation

Bonciolini, Giacomo; Noiray, Nicolas

doi:10.33737/gpps19-tc-091

Cited by 5 publications

(12 citation statements)

References 53 publications

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“…Regarding opportunities for future work, we note that an effect worth exploring is that of the speed with which the forcing conditions are varied. Recent thermoacoustics experiments by Bonciolini & Noiray (2019) have shown that it is possible to dodge a supercritical Hopf bifurcation if the bifurcation parameter can be varied sufficiently quickly. It is thus reasonable to expect an analogous phenomenon occurring in forced synchronization, whereby it may be possible to dodge certain T 2 or T 3 states en route to complete synchronization if f f or f can be varied sufficiently quickly.…”

Section: Discussionmentioning

confidence: 99%

Forced synchronization of quasiperiodic oscillations in a thermoacoustic system

et al. 2019

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In self-excited combustion systems, the application of open-loop forcing is known to be an effective strategy for controlling periodic thermoacoustic oscillations, but it is not known whether and under what conditions such a strategy would work on thermoacoustic oscillations that are not simply periodic. In this study, we experimentally examine the effect of periodic acoustic forcing on a prototypical thermoacoustic system consisting of a ducted laminar premixed flame oscillating quasiperiodically on an ergodic $\mathbb{T}^{2}$ torus at two incommensurate natural frequencies, $f_{1}$ and $f_{2}$. Compared with that of a classical period-1 system, complete synchronization of this $\mathbb{T}_{1,2}^{2}$ system is found to occur via a more intricate route involving three sequential steps: as the forcing amplitude, $\unicode[STIX]{x1D716}_{f}$, increases at a fixed forcing frequency, $f_{f}$, the system transitions first (i) to ergodic $\mathbb{T}_{1,2,f}^{3}$ quasiperiodicity; then (ii) to resonant $\mathbb{T}_{1,f}^{2}$ quasiperiodicity as the weaker of the two natural modes, $f_{2}$, synchronizes first, leading to partial synchronization; and finally (iii) to a $P1_{f}$ limit cycle as the remaining natural mode, $f_{1}$, also synchronizes, leading to complete synchronization. The minimum $\unicode[STIX]{x1D716}_{f}$ required for partial and complete synchronization decreases as $f_{f}$ approaches either $f_{1}$ or $f_{2}$, resulting in two primary Arnold tongues. However, when forced at an amplitude above that required for complete synchronization, the system can transition out of $P1_{f}$ and into $\mathbb{T}_{1,2,f}^{3}$ or $\mathbb{T}_{2,f}^{2}$. The optimal control strategy is to apply off-resonance forcing at a frequency around the weaker natural mode ($f_{2}$) and at an amplitude just sufficient to cause $P1_{f}$, because this produces the largest reduction in thermoacoustic amplitude via asynchronous quenching. Analysis of the Rayleigh index shows that this reduction is physically caused by a disruption of the positive coupling between the unsteady heat release rate of the flame and the $f_{1}$ and $f_{2}$ acoustic modes. If the forcing is applied near the stronger natural mode ($f_{1}$), however, resonant amplification can occur. We then phenomenologically model this $\mathbb{T}_{1,2}^{2}$ thermoacoustic system as two reactively coupled van der Pol oscillators subjected to external sinusoidal forcing, and find that many of its synchronization features – such as the three-step route to $P1_{f}$, the double Arnold tongues, asynchronous quenching and resonant amplification – can be qualitatively reproduced. This shows that these features are not limited to our particular system, but are universal features of forced self-excited oscillators. This study extends the applicability of open-loop control from classical period-1 systems with just a single time scale to ergodic $\mathbb{T}^{2}$ quasiperiodic systems with two incommensurate time scales.

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Section: Discussionmentioning

confidence: 99%

Forced synchronization of quasiperiodic oscillations in a thermoacoustic system

et al. 2019

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“…Bonciolini et al [10] experimentally and numerically verified the tipping-delay phenomenon in rate-dependent thermoacoustic systems driven by Gaussian white noise. Subsequently, they also found that thermoacoustic instabilities can be circumvented when the rate of parameter change is fast enough [11]. Further, Zhang et al [12,13] considered the correlation time of noise, extended the above findings to systems excited by Gaussian colored noise, and obtained the effect of noise correlation time coupled with the rate of parameter change on thermoacoustic systems.…”

Section: Introductionmentioning

confidence: 97%

Rate-dependent tipping and early warning in a thermoacoustic system under extreme operating environment

Zhang

Liu

et al. 2021

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Thermoacoustic instability has been an important challenge in the development of highperformance combustion systems, as it can have catastrophic consequences. The process of a sudden change in the dynamical behaviour of a thermoacoustic system from a low to a high amplitude thermoacoustic instability, actually entails as a tipping point phenomenon.It has been found that when rate-dependent parameters are considered, a tipping-delay phenomenon may arise, which helps in the control of undesirable states that give rise to thermoacoustic instabilities. This work aims at understanding rate-dependent tipping dynamics of the thermoacoustic system with both time-varying parameters and a non-Gaussian Lévy noise. The latter better describes the severe operating environment of such systems than simpler types of noise. Through numerical simulations, the tipping dynamical behaviour is analysed by considering the rate-dependent parameters coupled with the main parameters of the Lévy noise, including the stability and skewness indices, and the noise intensity. In addition, we investigate the effectiveness of early warning indicators in rate-dependent systems under Lévy noise excitation, and uncover a relationship between warning measures and the rate of change in the parameters. These results inform and enlighten the development and design of power combustion devices, and also provide researchers and engineers with effective ideas to control thermoacoustic instability and the associated tipping dynamics.

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“…These range from ships experiencing wave induced time varying restoring moments [79], through multiple scale dynamics [9], to investigating the effects of a moving mass on structures [76], or the switching between different working regimes [23], or milling stability with time dependent parameters [17]. Tipping events are sudden changes accompanying parameter drifts, and our method is useful to apply in such cases (see, e.g., [47,72]), too, including the avoidance of instability via fast enough rates of the parameter drift [6,85]. In analogy with climate sensitivity, parameter sensitivity or model uncertainty can be defined in mechanical systems, too (see, e.g., [3,49]), concepts to which the ensemble approach proposed here might be natural to extend.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…The nodes become converted into elliptic ones, with eigenvalues ±i √ 2. These snapshot elliptic points (SEPs) are, from (6), given by:…”

Section: Snapshot Hyperbolic and Elliptic Pointsmentioning

confidence: 99%

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Climate change in mechanical systems: the snapshot view of parallel dynamical evolutions

2021

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We argue that typical mechanical systems subjected to a monotonous parameter drift whose timescale is comparable to that of the internal dynamics can be considered to undergo their own climate change. Because of their chaotic dynamics, there are many permitted states at any instant, and their time dependence can be followed—in analogy with the real climate—by monitoring parallel dynamical evolutions originating from different initial conditions. To this end an ensemble view is needed, enabling one to compute ensemble averages characterizing the instantaneous state of the system. We illustrate this on the examples of (i) driven dissipative and (ii) Hamiltonian systems and of (iii) non-driven dissipative ones. We show that in order to find the most transparent view, attention should be paid to the choice of the initial ensemble. While the choice of this ensemble is arbitrary in the case of driven dissipative systems (i), in the Hamiltonian case (ii) either KAM tori or chaotic seas should be taken, and in the third class (iii) the best choice is the KAM tori of the dissipation-free limit. In all cases, the time evolution of the chosen ensemble on snapshots illustrates nicely the geometrical changes occurring in the phase space, including the strengthening, weakening or disappearance of chaos. Furthermore, we show that a Smale horseshoe (a chaotic saddle) that is changing in time is present in all cases. Its disappearance is a geometrical sign of the vanishing of chaos. The so-called ensemble-averaged pairwise distance is found to provide an easily accessible quantitative measure for the strength of chaos in the ensemble. Its slope can be considered as an instantaneous Lyapunov exponent whose zero value signals the vanishing of chaos. Paradigmatic low-dimensional bistable systems are used as illustrative examples whose driving in (i, ii) is chosen to decay in time in order to maintain an analogy with case (iii) where the total energy decreases all the time.

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Bifurcation Dodge: Avoidance of a Thermoacoustic Instability under Transient Operation

Cited by 5 publications

References 53 publications

Forced synchronization of quasiperiodic oscillations in a thermoacoustic system

Forced synchronization of quasiperiodic oscillations in a thermoacoustic system

Rate-dependent tipping and early warning in a thermoacoustic system under extreme operating environment

Climate change in mechanical systems: the snapshot view of parallel dynamical evolutions

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